Ring clamp stress 1

[45ao45]

Hi all, I am attempting to work out bolt clamping force required to ensure the gaskets in a shell and tube exchanger girth joints. The joints aren’t the typical ASME Weld neck design, instead there are two bolted half rings that encompass the girth flange (see picture attached). I discovered that I need higher bolt forces to seat the gaskets, and want to ensure I don’t damage the clamps in the process. I am happy with the thread strip check, and shear stress, though I am struggling with bending check. Does anyone have any insights on how to perform a ring bending stress? Thanks for any advice.

 

[Doug Hunter]

Do you have a picture/sketch of the same view but of the complete installation with all parts? We need to be clear on how all the forces are acting.

 

[45ao45]

Do you have a picture/sketch of the same view but of the complete installation with all parts? We need to be clear on how all the forces are acting.

Hi Doug Hunter, I have attached a sketch of the clamp installed joining the shell and shell cover of the exchanger. The bolt is compressed by torquing and in turn stretches the clamp.
I am interested in how to work out the bending stress on the clamp itself from the bolt load.
I am comfortable with groove on the shell cover (head in sketch) following ASME 8 MA-2. I also worked out the shear on the clamp to groove using TEMA backing ring shear check. It’s the bending stress of the “ring” clamp that I am struggling with. Appreciate any insights!

 

[Doug Hunter]

Hi 45ao45,

The best way to calculate the bending stress is with FEA, but I'll assume that you're trying to avoid that and get a quicker answer. That being said, here is one way to get a quick answer: I would break the clamp into 3 sections: 1 for each of the 2 vertical sections and 1 for the longer horizontal section, and apply beam theory to each section independently. This would assume that you "roll out" the 180-degree curvature into a flat part. I think that you'll get a conservative result because the half-circle part would resist bending a little better than the flat part, although I would expect the stresses to be similar between the 2 cases. For the 2 vertical sections, you have a force acting at the end of a cantilever that is resisted by a moment at the ends of the horizontal section. Use the 1st example at the reference below. The 2 moments at the ends of the horizontal section would need to be equal and opposite, so you might need to assume the higher of the 2 vertical results. For the horizontal section, use the 5th or 10th example at the reference below.

You can get the equations at this reference: https://mechanicalc.com/reference/beam-deflection-tables

Max tensile stress = M/Z, M is the moment, Z is the section modulus = b(h^2)/6 at any cross section. The moment and stress stay constant along the length of the beam, but the amount of deflection varies according to the length of the beam.

 

[Stress_Eng]

If you want to do a hand calc, there's a few ways you can do it. For the cylindrical section in the middle, I would look at using cylinder theory. Depending on the radial length of the two circular end plates (from bolt contact radius to the mid radius of the outer cylinder for the bolted plate and contact radius to mid outer cylinder radius for the other circular plate), I'd look at using circular plate theory. Both the cylinder and circular plate methods are in Roark. I've come across situations where, if the radial length of the circular plate is short (giving minimal circumferential distributed moment over its radial length), you can look at the end plate as a ring (again in Roark). All you have to do is equate the boundary conditions at the ends of the cylinder (cylinder to plate). Based on a FBD, what needs to be equal in magnitude are the contact forces at the bolts and at the circular plate on the other side.